The small neighborhood houses high ranking officials and some of India’s wealthiest businessmen. No wonder it’s one of the most expensive districts in the world.

After Narendra Modi was elected in May 2014, he and dozens of his newly-minted ministers followed the longtime tradition of high-ranking Indian government officials: They moved into stately homes in the New Delhi neighborhood of Lutyens.

Located in the heart of Delhi, a city where snarling traffic abuts dusty streets teeming with people, the Lutyens Bungalow Zone, or LBZ as it is called, is 10 square miles of greenery, wide boulevards, gates and hedges. Only about 60 or 70 of the homes in the neighborhood are privately owned. The rest belong to the government, which doles out the low-slung white bungalows to India’s top ministers, justices and military brass. The government homes are free—as with the White House, officials must move out when their terms end.

Along with the prime minister’s estate and the president’s estate, Lutyens is home to Arun Jaitley, minister of finance, corporate affairs and information and broadcasting, and Rajnath Singh, minister of home affairs. Some of India’s wealthiest businessmen, including Bharti Enterprises conglomerate chief Sunil Mittal and real-estate developer K.P. Singh, own homes here as well. Many of the privately held homes have been passed down through families for generations.

“It’s the country’s power center,” says Ashutosh Limaye, head of research at JLL India, a real estate consultancy. “Having a house in that area definitely makes a statement.”

Lutyens homes, which are typically at least 5,000 square feet and sit on an acre or two of land, are rarely on the market. The minimal turnover has caused real-estate values to increase at a near constant over the past two decades, unaffected by the overall economy in India, making LBZ one of the most expensive pockets of real estate in the world. Local real-estate agents say many LBZ homes are valued at anywhere from $25 million to nearly $100 million.

In recent months, Indian media company Essel Group, headed by Subhash Chandra, bought a bungalow on nearly 3 acres for approximately $48 million. Last year, Rajiv Rattan, chairman of RattanIndia Power, bought a 10,000-square-foot bungalow on Amrita Shergill Marg, one of the most prestigious streets in Lutyens, for about $35 million.

In a city of 25 million, Lutyens is one of the few pockets of ample greenery, where residents enjoy a plethora of parks and gardens, says Akash Puri, senior vice president at North India Sotheby’s International Realty. The Delhi Golf Club, on the eastern side of LBZ, and the Delhi Gymkhana Club, a social club that opened in 1913, both have 30-year waiting lists, Mr. Puri says. Lodhi Gardens, one of Delhi’s most familiar green spaces, backs up to the well-known street of Amrita Shergill, where Mr. Rattan lives. Khan Market, a shopping street with jewelry shops, boutiques and upscale restaurants, is down the road.

The area is named after Edwin Lutyens, the British architect who is considered an important contributor to the Arts & Crafts movement. He was commissioned by the British government to design the new capital for imperial leaders between 1912 and 1930, after the British decided to move the country’s capital to Delhi from Kolkata. In keeping with Mr. Lutyens’s style, many of the homes here have large gardens and classical elements such as pediments and columned verandas.

In 1988, the Indian government essentially put a freeze on Lutyens development, allowing no new construction. The building ban means Lutyens has the lowest density in Delhi, to the chagrin of some city dwellers who say the neighborhood is underused. The construction rules also ensure the footprints of homes remain the same—meaning a 1,000-square-foot home can be renovated, but never include an addition. “What you see today will remain that way,” says Anshuman Magazine, chairman of real estate services company CBRE India. “You don’t need to worry about your neighbor putting up something to block your view.”

While homes at these prices would typically include a number of modern amenities, many Lutyens bungalows can be quite simple. In some cases, they need a lot of repair. That is because sky-high prices for LBZ homes have led to family infighting. Many of the homes that have been passed down through generations have multiple owners—and attempting to renovate a property, sell it or even agree on a valuation can lead to legal disputes.

Mr. Magazine gives the example of two sons who co-own a bungalow, with one son’s family living in New Delhi, while the other son lives abroad. “One son doesn’t want to move out of the place because if they were to sell they can’t afford to re-buy in the same location. But the other son wants to sell,” he says, adding that if the home is valued at, say, $50 million, it is unlikely that the first son could afford to buy out the second son. If these cases are taken to court, they can take years to resolve, while the homes fall into disrepair in the interim.

Residents say the area’s upsides—central location and ample land—compensate for any drawbacks. Businessman Ramnik Chopra lives in a Lutyens two-story home that he co-owns with his cousin. The 12-bedroom, 12-bathroom home with marble flooring, a private yard and double-height ceilings has been in the family since 1959. While there are newer homes in Delhi, Mr. Chopra says they don’t have yards or parking space like Lutyens does. “I could never think of living anywhere else,” he says.